Ballistic MOS Model (BMM) Considering Full 2D Quantum Effects

As the channel length of MOSFETs is shrunk to below 50 nm, 2D quantum mechanical (QM) e®ects becomes profound on both the carrier con¯nement in the transverse direction to the channel and the carrier transport, mainly ballistic and tunneling, along the channel. A compact MOS model which incorporates the physicsbased correction of 2D QM e®ects on the surface inversion charge density and ballistic transport is developed. The model has been applied to various MOS devices with gate length ranging from 45nm to 14nm and excellent agreement with published measurement data is achieved. It is proposed for the ¯rst time that WKB theory can be explored to model the subband lowering in the con¯ned dimension because of the open boundary on the other dimension. An empirical formula for 2D-QM-corrected threshold voltage is provided. Mobility dependence on gate bias is investigated and modeled.